Don't believe it's Rosemary(note the graft).
Perhaps a Westringia?

That's funny. I never noticed the graft before. I was too busy squinting at the leaves.
Can I get Rosemary to do this?

It should work, I see them for sale in garden centers from time to time.

Rosemary topiaries are very common.

Definitely not rosemary but I have seen rosemary in similar shapes. If you google "topiary" or "make topiary" you'll get more info on the how-to's of it. You could also try "herbal topiary" if you want to do it with herbs like rosemary.

FataMorgana

For topiary, make sure you get an upright variety of rosemary, as opposed to prostrate.

I'm not sure I've ever seen an upright one. I had one that sprawled on the ground almost like a groundcover, then another that's upright but more like a bush. I'll have to "look under their skirts" before buying I guess?

Tuscan for example

Here is a link that might be useful: {{gwi:135090}}

That looks like what I have! If I start cuttings, will they be the same?

As a side-note, I can't hardly make a poultry dish without Rosemary unless it's mexican food. I should probably take cuttings and grow more Rosemary regardless, since I keep picking my plants almost clean!

Yes, all clones (cuttings) should be identical to the parent plant.

It is Dwarf Myrtle, smells great like Rosemary does.

Myrtus communis 'compacta'

You can't get rosemary to grow like that because it needs a strong, woody trunk to hold up the top growth, and rosemary isn't like that.

But rosemary is very easy to grow from cuttings. Just take cuttings and put them in a pot and water them and they'll root.

About the Tuscan blue - thanks for posting the pic, I have a couple of small ones. I like this one because it has bright blue flowers that are a lot larger than other rosemaries.

Yes, you can either purchase or develop rosemary as a standard, but I think what you have in the picture is common myrtle.

I'll try it with both! I already have some Rosemary, but I'll have to try to find Myrtle. I'm not sure I've ever seen it for sale before?